Question

parallelogram f is a scaled copy of parallelogram e. parallelogram e has side - lengths 2\frac{1}{5} and 5. parallelogram f has side - lengths 2\frac{3}{4} and d. what is the value of d?

Explanation:

Step1: Find the scale - factor

Since the two parallelograms are scaled copies, the ratios of corresponding sides are equal. Let the scale - factor be $k$. We can find the scale - factor by comparing the corresponding non - parallel sides. The ratio of the non - parallel sides is $k=\frac{2\frac{3}{4}}{2\frac{1}{5}}$. First, convert the mixed numbers to improper fractions: $2\frac{3}{4}=\frac{2\times4 + 3}{4}=\frac{11}{4}$ and $2\frac{1}{5}=\frac{2\times5+1}{5}=\frac{11}{5}$. Then $k=\frac{\frac{11}{4}}{\frac{11}{5}}=\frac{11}{4}\times\frac{5}{11}=\frac{5}{4}$.

Step2: Calculate the value of $d$

We know that $d$ corresponds to the side of length 5 in parallelogram $E$. Using the scale - factor, we have $d = 5\times k$. Substitute $k=\frac{5}{4}$ into the equation: $d=5\times\frac{5}{4}=\frac{25}{4}=6\frac{1}{4}$.

Answer:

$6\frac{1}{4}$